Question

4. Find the square roots of the following numbers by the Prime Factorisation Method.
(i) 729
(ii) 400
(iii) 1764
(v) 4096
(V) 7744
(vi) 9604
(vii) 5929
(viii) 9216
(ix) 529
(x) 8100

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Answer 1

(i) 729 = 3 × 3 × 3 × 3 × 3 × 3

√729 = √(3 × 3 × 3 × 3 × 3 × 3)

= 3 × 3 × 3

= 27

==========================

(ii) 400 = 2 × 2 × 2 × 2 × 5 × 5

√400 = √(2 × 2 × 2 × 2 × 5 × 5)

= 2 × 2 × 5

= 20

==========================

(iii) 1764 = 2 × 2 × 3 × 3 × 7 × 7

√1764 = √(2 × 2 × 3 × 3 × 7 × 7)

= 2 × 3 × 7

= 42

==========================

(iv) 4096 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2

√4096 = √(2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2)

= 2 × 2 × 2 × 2 × 2 × 2

= 64

==========================

(v) 7744 = 2 × 2 × 2 × 2 × 2 × 2 × 11 × 11

√7744 = √(2 × 2 × 2 × 2 × 2 × 2 × 11 × 11)

= 2 × 2 × 2 × 11

= 88

==========================

(vi) 9604 = 2 × 2 × 7 × 7 × 7 × 7

√9604 = √(2 × 2 × 7 × 7 × 7 × 7)

= 2 × 7 × 7

= 98

==========================

(vii) 5929 = 7 × 7 × 11 × 11

√5929 = √(7 × 7 × 11 × 11)

= 7 × 11

= 77

==========================

(viii) 9216 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 3 × 3

√9216 = √(2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 3 × 3)

= 2 × 2 × 2 × 2 × 2 × 3

= 96

===========================

(ix) 529 = 23 × 23

√529 = √(23 × 23)

= 23

===========================

(x) 8100 = 2 × 2 × 3 × 3 × 3 × 3 × 5 × 5

√8100 = √(2 × 2 × 3 × 3 × 3 × 3 × 5 × 5)

= 2 × 3 × 3 × 5

= 90

===========================

THANKS.

Answer 2

∣ ❥Ꭺɴꮪꮃꭼꭱ࿐ ∣

(i) 729

$\sqrt{729} = \sqrt{3 \times 3 \times 3 \times 3 \times 3 \times 3}$

$= 3 \times 3 \times 3$

$= 27$

ii)400

$\sqrt{400} = \sqrt{2 \times 2 \times 2 \times 2} \times 5 \times 5$

$= 2 \times 2 \times 5$

$= 20$

iii) 1764

$\sqrt{7164} = \sqrt{2 \times 2 \times 3 \times 3 \times 7 \times 7}$

$= 2 \times 3 \times 7$

$42$

$same \: method \: used \: in \: other \: equation \:$

$thank \: u \:$

$have \: a \: great \: day \: ahead \:$

$llovelypoisonll ✨$